Question

Aflați toate nr. x nat. pentru care fracția 6 supra 2x+1

Answer 1

2x+1<6
2x<5
x<5/2
x=0,1,2

Answer 2

$\frac{6}{2x+1} \ ; x \in N \\\\ 1) \ 2x+1=5 \\\\ 2x=5-1 \\\\ 2x=4 \ |:2 \\\\ \boxed{x=2}$

$2) \ 2x+1=4 \\\\ 2x=4-1 \\\\ 2x=3 \\\\ x=\frac{3}{2} \not\in N \\\\ 3) \ 2x+1=3 \\\\ 2x=3-1 \\\\ 2x=2 \ |:2 \\\\ \boxed{x=1} \\\\ 4) \ 2x+1=2 \\\\ 2x=2-1 \\\\ 2x=1 \\\\ x=\frac{1}{2} \not\in N \\\\ 5) \ 2x+1=1 \\\\ 2x=1-1 \\\\ 2x=0 \\\\ \boxed{x=0} \\\\ x \in N \\\\\\ \boxed{\boxed{x=\{0;1;2\}}}$